The value of ∫$$sin$$⁡$$x3dx$$ is

Correct option is 232−x2/3cos⁡x1/3+2x1/3sin⁡x1/3+C

Questions

The value of $\int \sin \sqrt[3]{x} d x$ is

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2−x2/3cos⁡x1/3+2x1/3sin⁡x1/3+C

32−x2/3cos⁡x1/3+2x1/3sin⁡x1/3+C

32−x2/3sin⁡x1/3−2x1/3cos⁡x1/3+C

none of these

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detailed solution

Correct option is B

Put x1/3=θ so that dx=3θ2dθ∴I=3∫θ2sin⁡θdθ=−3θ2cos⁡θ+6∫θcos⁡θdθ=−3θ2cos⁡θ+6θsin⁡θ−6∫sin⁡θdθ=32−θ2cos⁡θ+6θsin⁡θ+C.

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The value of ∫sin⁡x3dx is

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The value of $\int \sin \sqrt[3]{x} d x$ is